Lily's Snack Shack used 7 bottles of ketchup. According to the problem, they used \(\frac{2}{3}\) as much mustard as ketchup.
To find the amount of mustard used, we need to calculate:
\[ \text{Mustard used} = \frac{2}{3} \times \text{Ketchup used} = \frac{2}{3} \times 7 \]
Now, we multiply:
\[ \frac{2}{3} \times 7 = \frac{2 \times 7}{3} = \frac{14}{3} \]
The fraction \(\frac{14}{3}\) can also be expressed as a mixed number. To convert this fraction:
- Divide 14 by 3, which equals 4 with a remainder of 2.
- Therefore, \(\frac{14}{3}\) can be expressed as \(4\) with a remainder of \(\frac{2}{3}\).
Thus, as a mixed number, it is:
\[ 4 \frac{2}{3} \]
In conclusion, Lily's Snack Shack went through \(\frac{14}{3}\) bottles of mustard, which can also be written as:
\[ \boxed{\frac{14}{3}} \text{ or } 4 \frac{2}{3} \]
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